In Exercises 105 and 106, use the position function s ( t ) = − 16 t 2 + 500 , which gives the height (in feet) of an object that has fallen for t seconds from a height of 500 feet. The velocity at time t = a seconds is given by lim t → a s ( a ) − s ( t ) a − t ⋅ A construction worker drops a full paint can from a height of 500 feet. When will the paint can hit the ground? At what velocity will the paint can impact the ground?
In Exercises 105 and 106, use the position function s ( t ) = − 16 t 2 + 500 , which gives the height (in feet) of an object that has fallen for t seconds from a height of 500 feet. The velocity at time t = a seconds is given by lim t → a s ( a ) − s ( t ) a − t ⋅ A construction worker drops a full paint can from a height of 500 feet. When will the paint can hit the ground? At what velocity will the paint can impact the ground?
Solution Summary: The author calculates the Velocity of a paint can when it touches the ground.
In Exercises 105 and 106, use the position function
s
(
t
)
=
−
16
t
2
+
500
,
which gives the height (in feet) of an object that has fallen for t seconds from a height of 500 feet. The velocity at time
t
=
a
seconds is given by
lim
t
→
a
s
(
a
)
−
s
(
t
)
a
−
t
⋅
A construction worker drops a full paint can from a height of 500 feet. When will the paint can hit the ground? At what velocity will the paint can impact the ground?
During Ricardo noticed an ink stain with a diameter of about 3 cm on the front of his teacher’s shirt. He then noticed that there was a pen in the pocket and that the ink blot was continuing to spread across the front of the teacher’s shirt. He estimated that the diameter of the ink blot seemed to be growing by about 0.5 cm every 2 minutes.
a) Write an equation for the RADIUS, r, of the ink stain, as a function of time, t. Assume that t = 0 represents the time that Ricardo first noticed the ink stain.
b) Write an equation showing the AREA, A, of the ink stain as a function of the time t. (Hint: It might help to first write A as a function of r. )
c) Draw a graph of the function A(t) for 10 minutes.
d) At what time is the area of the ink stain about 25 square centimeter? Show how you answer this question. (i.e. ”I found it using desmos” is not sufficient)
A Ferris wheel has a diameter of 40 meters and rotates at a constant speed completing one full revolution every 2 minutes. If a person gets on the Ferris wheel at the bottommost point, express the person's height above the ground as a function of time, assuming the center of the Ferris wheel is at ground level.
Answer: The Ferris wheel has a diameter of 40 meters, which means the radius (r) is half of the diameter, i.e., (r = 20) meters. The Ferris wheel completes one full revolution every 2 minutes. The period (T) of the Ferris wheel is the time it takes to complete one full revolution. In this case, T = 2 minutes. The angular frequency (w) can be calculated using the formula (w = 2/?). Substituting the given value for (T): w = 2/? = ? radians per minute. Now, the height (h) of the person above the ground as a function of time (t) can be expressed using a sine function. The general form of a sine function is h(t) = A sin(wt+ϕ)+C where: - A is the amplitude (half the range of the…
Let P = (x,y) be a point on the graph of y x-12.
Express the distance, d, from P to the origin as a function of the point's x-coordinate.
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